On "Fast Money," Cooperman said that he had not been "keen on their financial policy."

With an estimated $121 billion in cash on its balance sheet, Apple did not announce a special dividend for 2012.

Cooperman acknowledged that nothing would likely replace Apple's wildly popular iPhone, but noted that other competitors, such as Samsung, would continue to challenge the company for dominance.

Google and Qualcomm, which Cooperman said was "more ubiquitous" and "not just Apple-dependent," stood to continue their strong performance.

However, Cooperman hasn't exited Apple, adding that Omega Advisors' positions in the company were "just not as big as we were before."

Trader disclosure: On Jan. 2, 2013, the following stocks and commodities mentioned or intended to be mentioned on CNBC's "Fast Money" were owned by the "Fast Money" traders: Jon Najarian is long STZ; Jon Najarian is long ALXN; Jon Najarian is long CMI; Jon Najarian is long COF; Jon Najarian is long MA; Jon Najarian is short AAPL; Jon Najarian is short NFLX; Jon Najarian is short VMW; Jon Najarian is long VIX CALL SPREADS; Steve Weiss is long QCOM; Steve Weiss is long TBF; Steve Weiss is long AIG; Steve Weiss is long BAC; Steve Weiss is long WLT; Steve Weiss is long C; Steve Weiss is long JPM; Steve Weiss is long M; Joe Terranova is long VRTS; Joe Terranova is long TJX; Joe Terranova is long AAPL; Joe Terranova is long GS; Joe Terranova is long MS; Joe Terranova is long SWN; Joe Terranova is long GLW; Joe Terranova is long DELL; Joe Terranova is long VZ; Joe Terranova is long XOM; Simon Baker is funds long IWM; Simon Baker is funds long AAPL; Simon Baker is funds long AMAT; Simon Baker is funds long BAC; Simon Baker is funds long BRCM; Simon Baker is funds long T; Simon Baker is funds long WFC; Simon Baker is funds long QCOM; Simon Baker is funds long MSFT; Simon Baker is funds long GOOG; Simon Baker is funds long CSCO; Simon Baker is funds long XLU; Simon Baker is funds long NOK; Dennis Gartman is long AUD; Dennis Gartman is long NZD; Dennis Gartman is short YEN; Dennis Gartman is long Gold in EUR/JPY Terms; Dennis Gartman is short EUR; Dennis Gartman is short YEN; Dennis Gartman is short Crude Oil; Dennis Gartman is short US 10Y Treasuries.